The White House has sent a list of changes it would like to see made to the health-care bill, but some Republicans say the White House should skip the middleman and negotiate directly with Democrats.

“Next step is really for the White House to sit down with Democrats, and discuss their asks and negotiate,” said a Senate GOP aide. “This is the legislative process. If they have suggestions, then now they need to negotiate.”

“If there's a need for some kind of interim step here to stabilize the market, we need a bill the president will actually sign,” McConnell said on CNN. “And I'm not certain yet what the president is looking for here, but I will be happy to bring a bill to the floor if I know President Trump would sign it.”

Democrats, though, are pushing back on the idea of additional talks, saying they already negotiated a fair deal.

“The next step is for Leader McConnell to put the bill that has the votes to pass on the Senate floor,” said a Senate Democratic aide. “It's in bad faith for the White House to come back with additional asks after being closely involved in the negotiations.”

“Look, this is a good compromise,” Schumer said. “It took months to work out. It has a majority. It has 60 senators supporting it. We have all 48 Democrats, 12 Republicans.”

Schumer on Sunday did not completely rule out continued talks after being pressed on the point.

Still, while the Democrats are not totally ruling out more talks, they caution that any changes to the agreement need to be constructive. And they view lifting the individual mandate for one year — a step requested by the White House — as moving in the wrong direction.

Democrats have been open to another issue raised by Trump, however. The president has said the deal should ensure that insurance companies do not benefit from payments, known as cost-sharing reductions (CSRs), that the legislation would extend for two years.

The bill already includes language that would require insurers to pass savings on to consumers in the form of a rebate or another mechanism, but lawmakers say that language could be strengthened.

But the White House’s list of demands goes beyond the payments to several changes that Democrats are likely to oppose.

In addition to lifting the individual mandate penalty for 2017, the proposed changes would lift for three years the penalty for employers who don’t offer coverage. The White House also wants to expand short-term health insurance plans and association health plans; Democrats fear those plans will offer less generous coverage and siphon healthy people away from ObamaCare.

The White House’s demands also include giving states “additional flexibilities” to waive ObamaCare rules, beyond what the deal already allows.

Alexander told reporters Monday that he supports all of the changes the White House has proposed, but it's up to them to negotiate.

"The White House has the ball right now," he said. "I'm for all of those things. The question is whether they can persuade Democratic senators to agree to that."

The current deal, aimed at stabilizing ObamaCare markets, funds the CSR payments, which are important for preventing premium hikes, while expanding waivers allowing states to innovate and change ObamaCare rules.

Conservative Republicans warn that continuing the payments is a “bailout” for insurers. The deal is seen as unlikely to move forward as a stand-alone bill, given that opposition.

Supporters of the legislation, though, are hopeful that it could be added to a government funding bill at the end of the year.